Abstract Algebra/Group Theory/Subgroup/Intersection of Subgroups is a Subgroup
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Let H1, H2, ... Hn be subgroups of Group G with operation
- with is a subgroup of Group G
with is a Group 
8. is associative on G. Group G's operation is 9. 3. 10. is associative on 8. and 9.
15. Choose 16. , , and 17. gH1−1 in H1, and gH2−1 in H2. G, H1, and H2 are groups 18. 19. G and H1 shares identity e 20. gH1−1 is inverse of g in G 19. and definition of inverse 21. Let gG−1 be inverse of g has in G 22. gG−1 = gH1−1 inverse is unique 22. gG−1 = gH2−1 similar to 21. 23. 24. g has inverse g−1 in